Origin of the ground-state energy of a particle in a potential well

In this paper, an apparently universal feature of the ground-state energy of a particle in a potential well is pointed out. Namely, by the example of an infinitely deep rectangular potential well, we clearly demonstrate that this energy, as well as the localization energy of a particle ensuing from the Heisenberg relation, is accumulated by the work of an external force against the particle pressure force on the well walls during compression of the particle substance and, correspondingly, its wave function ψ from unbounded free space to the finite volume of the well. This work is exactly equal to the particle ground-state energy.     

Longitudinal-optical phonon effects on the binding energy of a hydrogenic impurity in a quantum well structure

Summary The polaron effect on the binding energy of a hydrogenic impurity in a semiconductor quantum well is calculated by a variational approach taking into account the quasi-two-dimensional and the realist structures of systems. For the finite potential barrier, a correction is obtained as a function of the well thickness and presents a maximum; its evolution is analogous to the binding energy.     

半导体量子阱中弱耦合磁极化子的性质

采用线性组合算符和改进的LLP变分法,研究了在考虑电子自旋情况下无限深量子阱中弱耦合磁极化子的性质。导出了弱耦合磁极化子的声子平均数、基态能量和电子自旋能量与磁极化子基态能量之比的绝对值的表达式。并对两种不同阱材料的量子阱进行了数值计算,结果表明:磁极化子的声子平均数随电子-LO声子耦合常数和阱宽的增加而增大,并且最终随着阱宽的增加而趋于体情况下的极限值;由于电子自旋能的作用使磁极化子的基态能量由不考虑电子自旋下的一条分裂为两条,并且它随阱宽和电子-LO声子耦合常数的增加而减小,随回旋共振频率(磁场)的增加而增大。电子自旋作用能否忽略由回旋共振频率和阱材料本身的性质决定。     

On the interaction of a beam of polar molecules with a static and a resonant RF field as a source of molecular interferences

A molecular beam interference model is presented based on a two-state interaction between a polar molecule and a resonant RF field as it occurs in the so-called C-field of a typical molecular beam electric resonant spectrometer. The treatment shows the onset of interferences in the beam transmission spectra as well as in its transverse profile. It is demonstrated how the molecular interferences are originated by the wavefunction phase shift introduced by the resonant RF field. Furthermore it is shown that for a given beam velocity and oscillating field frequency the fringes’ visibility depends on the strength of the RF field, i.e. the Rabi frequency, in the transmission spectra. Likewise the presence of a RF field gradient in the perpendicular beam direction gives rise to a peak structure in the transverse beam profile. The theoretical model was applied to simulate a variety of beam transmission spectra under resonant conditions as well as some experimental data already published by our group showing a satisfactory agreement between experimental and simulated data. Finally, the potentiality of this internal state molecular interferometer to carry out studies in matter-wave interferometry is remarked.     

Invariant relation in the problem of size quantization in a self-consistent potential near the semiconductor boundary

The invariant relation in the eigenvalue problem is found for a one-dimensional nonlinear integrodifferential operator acting on the normalized eigenfunctions. The invariance of the obtained relationship follows, in particular, from the fact that it is independent of the detailed form of the operator. This problem arises in the physics of a two-dimensional electron system near the semiconductor boundary, where the potential well is formed, on the one hand, by a high potential barrier at the boundary and, on the other, by the intrinsic electric field screened by two-dimensional electrons filling the well. The invariant relates the energy of the size-quantization level to the average size of electron wave function in the well.     

Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

In this paper, the analytical solutions of Schr¨odinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker–Planck equation known as the Klein–Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr¨odinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.     

Transport theory for quantum wells with an electric field across the well: a new concept for a transistor

The transport properties of a two-dimensional electron gas in a quantum well with infinite barriers and with an electric field across the well as perturbation is calculated for zero temperature. Background impurity doping, remote impurity doping and interface roughness scattering are considered. The effects which are linear in the electric field are calculated. We suggest an experiment to measure the differences in the interface roughness scattering at the two interfaces of the quantum well by the electric field effect. We also discuss a possible device application of the field effect and describe a transistor working at the metal-insulator transition.     

Unexpected features in the magnetoresistance of a quantum well at room temperature

Well-resolved oscillations are reported in the resistivity of an InGaAs quantum well as a function of applied magnetic field below 1 Tesla. The oscillations are observed at room temperature and their magnetic field position depends on the component of the magnetic field in the plane of the well. Because of these unusual properties, the results cannot be due to bound states within the well but it is suggested that they can be explained by quantised states lying above the well in energy. The condition for the formation of the states is satisfied at lower magnetic fields than for normal Landau levels and the states are separated by larger energy intervals.     

Effect of the anomalous dispersion on the optical characteristics of a quantum well

The frequency dependence of the optical characteristics of a quantum well (reflectance, transmittance, and absorbance) in the vicinity of the interband resonance transitions is studied for the case of two closely spaced excited levels. A wide quantum well in a strong magnetic field directed perpendicular to the surface of the quantum well and an incident monochromatic wave are considered. Allowances are made both for the difference in the refractive indices of the barriers and the quantum well and for the spatial dispersion of the light wave. It is shown that, at long radiative lifetimes of the excited states (as compared to the nonradiative lifetimes), the frequency dependence of the light reflectance near the resonance interband transitions is primarily determined by a curve similar to that of the anomalous dispersion of the refractive index. As the lifetimes level off, the contribution of this curve decreases and becomes negligible when the lifetime ratio reverses. It is also shown that the transmittance and absorbance of light do not exhibit a frequency dependence resembling the anomalous dispersion.     

抛物量子阱中束缚极化子的极化势和结合能

利用改进的Lee-Low-Pines(LLP)方法,用变分法计算了无限深抛物量子阱中同时考虑与体纵光学声子和界面纵光学声子相互作用的束缚极化子的极化势和结合能.数值计算得出:阱宽较大时极化势很小,阱宽较小时极化势较大,所以对于较窄的抛物阱必须考虑极化势.对于给定阱宽的抛物阱,随着远离阱中心极化势迅速减小,当到达阱的界面附近极化势又开始增大.阱宽较小时,束缚极化子的结合能随着阱宽L的增大而急剧减小;阱宽较大时,结合能减小的非常缓慢,最后接近体材料中的三维值.     

Escape by diffusion from a square well across a square barrier

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time. In the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by Kramers for a curved well and a curved barrier. An approximate analytic formula is derived for the outward time-dependent probability current in terms of the width and depth of the well and the width and height of the barrier. A similar expression holds for the complete probability distribution.     

Study of the H chemisorption on a Cu surface by the recursion method

The electron density of states and the chemisprption energy have been calculated for the case of H on a Cu(111) surface, by means of the recursion method in connection with the continued fraction technique, in a self-consistent Hartree-Fock scheme. The Slater-Koster parameters existing in literature for Cu have been used, while a parametrized form has been taken for the H-metal interaction. The relative role of the d-bands and of the s-band have been investigated. It is shown how, by taking into account the importance of the s-band in the chemisorption process, it is possible to have results which fit well experimental results as well as other theoretical calculations.     

On the formation of a potential well for a nonferromagnetic conductor in a variable magnetic field

We consider the nonlinear ponderomotive effect produced by a phase shift between rapidly oscillating magnetic-field components. It is shown that the superposition of the fields leads to the formation of a potential well and to a significant increase in the force acting on a nonferromagnetic conductor.M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 93–98, September, 1994.     

Electronic properties of a quantum ring perturbed with a quantum well in the presence of perpendicular magnetic flux

Here, we study the effects of the number of sites, quantum ring radius and potential well depth on the energy levels, persistent current, magnetic susceptibility and density of states (DOS) of a quantum ring with a quantum well within its circumstance in a magnetic flux perpendicular to its plane. We show that, for small radius quantum ring systems, there are periodic local gaps along the magnetic flux axis in the DOS plots and along the axis ‘energy’. For large radius quantum ring systems, a uniform gap along the energy axis exists and along the phi axis nothing changes. In quantum rings with a quantum well in their circumstance, by using the large confining potential, we can create uniform gaps in the Energy–phi plane. The energy eigenvalues, persistent current and magnetic susceptibility decrease by increasing the confining potential. A quantum ring even with a very small confining potential in its circumstance can sensibly decrease the persistent current and magnetic susceptibility, although it may do not change the energy eigenvalues and DOS maximum considerably. Thus, by using the abovementioned parameters, we are able to tune the DOS, persistent current, magnetic susceptibility and energy levels, desirably.     

Tilted magnetic field effect on the subbands of a GaAlAs diode with a GaAs quantum well

We have calculated the subbands in the GaAs quantum well at the n-side of the junction in a Ga_1−xAl_xAs diode. We show that the density of carriers confined in the quantum well increases by the increasing magnetic field strength but also decreases depending on the magnetic length. We have observed oscillatory behavior of the density of carriers due to the in-plane magnetic field.     

Enhanced diffraction from a grating on the surface of a negative-index metamaterial

We show by numerical simulation as well as by measurements on negative-index metamaterial wedge samples, that the unavoidable stepping of the refraction interface-due to the finite unit-cell size inherent to metamaterials-can give rise to a well-defined diffracted beam in addition to the negatively refracted beam. The direction of the diffracted beam is consistent with elementary diffraction theory; however, the coupling to this higher order beam is much larger than would be the case for a positive index material. The results confirm recent theoretical predictions of enhanced diffraction for negative-index grating surfaces.     

Determination of the quantized velocity of a single photon confined into a one-dimensional cavity

Within a standing-wave approach, we determine the quantized velocity of a single photon in a one-dimensional cavity by considering the photon as an ultrarelativistic particle of non-zero rest-mass. As a matter of fact, this ultrarelativistic nature is regarded as well as the mathematical expression involving the photon modes in the cavity, and de Broglie relationship for the wave-particle dualism.     

Optical detection of the Aharonov-Bohm effect on a charged particle in a nanoscale quantum ring

We study spectroscopically the current produced by a charged particle moving in a nanosize semiconductor quantum ring subject to a perpendicular magnetic field. Several Aharonov-Bohm oscillations are observed in the emission of a charged exciton confined in a single ring structure. The magnetic field period of the oscillations correlates well with the size of the rings.     

Study of the Interaction of Plasma with Beryllium That Is a Candidate Material for the First Wall of a Fusion Reactor

The experimental conditions for treatment of a candidate material of the first wall, beryllium, by the plasma have been determined. The plasma parameters obtained using the simulator with a plasma-beam setup during the irradiation of samples as well as the results of material studies obtained by scanning electron microscopy and energy-dispersion analysis of the beryllium surface layer have been considered.     

Parameter-dependent third-order optical nonlinearity in a CdSe/ZnS quantum dot quantum well in the vicinity of a gold nanoparticle

The nonlinear optical properties of the CdSe/ZnS quantum dot quantum well (QDQW) in the vicinity of a spherical metal nano-particle (MNP) have been described. The third-order nonlinear optical susceptibility induced by the transition between E₁ (inside the well) and E₂ (outside the well) has been calculated for the third-harmonic generation (THG) under the effective mass approximation and modified by the local field theory. The parameters-dependent third-order nonlinear optical susceptibility for the THG has been specifically explored and the influence of the distance between the QDQW and the MNP on the third-order susceptibility for the THG in the system has been shown and analyzed.